Graham Potter's side had picked up just one point from its opening two games against Salzburg and Dinamo Zagreb, but victory at Stamford Bridge against the Serie A champion has revived the Blues' bid to reach the knockout stages.
Fofana scored his first goal for the club since joining from Leicester City in September after 24 minutes, slotting home after a goalmouth scramble.
Aubameyang and James, who set up the former's strike, made sure of the three points in the second half as Chelsea made it back-to-back wins following the weekend triumph over Crystal Palace in the Premier League.
Ciprian Tatarusanu kept out Mason Mount's whipped effort from outside the penalty area after four minutes, while the Milan goalkeeper pawed over Thiago Silva's header midway through the first half.
Tatarusanu denied Silva again soon after, yet the rebound made its way into the path of Fofana, who stroked home to put the Blues ahead.
Mount saw an effort ruled out for offside as Chelsea continued to dominate, although only a smart stop from Kepa Arrizabalaga prevented Rade Krunic from pulling Milan level on the stroke of half-time.
Former Rossoneri youth player Aubameyang doubled the Blues' advantage 11 minutes after the restart with a close-range finish from James' sublime cross.
James wrapped up the scoring five minutes later, the England international slamming into the roof of Tatarusanu's net after being played in by Raheem Sterling.